Semicontinuity of Betweenness Functions

Authors

Paul Bankston, Marquette UniversityFollow
Aisling McCluskey, National University of Ireland * Galway
Richard J. Smith, University College Dublin

Document Type

Article

Language

eng

Publication Date

9-1-2018

Publisher

Elsevier

Source Publication

Topology and its Applications

Source ISSN

0166-8641

Abstract

A ternary relational structure〈X,[⋅,⋅,⋅]〉, interpreting a notion of betweenness, gives rise to the family of intervals, with interval [a,b] being defined as the set of elements of X between a and b. Under very reasonable circumstances, X is also equipped with some topological structure, in such a way that each interval is a closed nonempty subset of X. The question then arises as to the continuity behavior—within the hyperspace context—of the betweenness function {x,y}↦[x,y]. We investigate two broad scenarios: the first involves metric spaces and Menger's betweenness interpretation; the second deals with continua and the subcontinuum interpretation.

Comments

Accepted version. Topology and Its Applications, Vol. 246 (September 1, 2018): 22-47. DOI. © 2018 Elsevier B.V. Used with permission.

Recommended Citation

Bankston, Paul; McCluskey, Aisling; and Smith, Richard J., "Semicontinuity of Betweenness Functions" (2018). Mathematics, Statistics and Computer Science Faculty Research and Publications. 621.
https://epublications.marquette.edu/mscs_fac/621